The government has a program working with precogs like in the minority report. However, what they have discovered is that any solid prediction made by the precogs cannot be changed. They are set in stone. There are some things that are fuzzy and indistinct which can have multiple interpretations, and so it is not known if they are a mutable future or just an imperfect viewing. But if something is predicted, it is set in stone.
What would the government find the most useful for this project. Unlike the movie, any crimes viewed are going to happen, no matter what those with pre-knowledge try to do to prevent it. So it wouldn't be any good as crime prevention. (though it might be good enough to help catch the perpetrators).
The precogs have limited control over what they see, though large events tend to affect them more consistently/clearly. The more personal or closer in proximity the more likely they'll get a reading. The more they try to focus on specific people or possible events, the 'hazier' it gets, up to complete garbage if the precog is under duress.
Merely seeing into the future would be enough of a reason for the program to exist, but how would a government be able to utilize this information for the "good of all". I'm asking as a public government program, not individuals trying to get money or power with it.